Advances On System Identification Techniques For DC-DC .
1Advances on System Identification Techniques forDC-DC Switch Mode Power Converter ApplicationsMaher Al-Greer1, Matthew Armstrong2, Mohamed Ahmeid2, Damian Giaouris21Teesside University, School of Science, Engineering and Design, Middlesbrough, UK2Newcastle University, School of Engineering, Newcastle upon Tyne, UKE-mail: m.al-greer@tees.ac.uk, matthew.armstrong@newcastle.ac.ukABSTRACTSystem identification is fundamental in many recent state-of-the-art developments in power electronic such as modelling,parameter tracking, estimation, self-tuning and adaptive control, health monitoring, and fault detection. Therefore, this paperpresents a comprehensive review of parametric, non-parametric, and dual hybrid system identification for DC-DC Switch ModePower Converter (SMPC) applications. The paper outlines the key challenges inherent with system identification for powerelectronic applications; speed of estimation, computational complexity, estimation accuracy, tracking capability, and robustness todisturbances and time varying systems. Based on literature in the field, modern solutions to these challenges are discussed in detail.Furthermore, this paper reviews and discusses the various applications of system identification for SMPCs; including healthmonitoring and fault detection.Index Terms— System Identification, Switch Mode Power Converters, Digital Control, Parametric Estimation, NonParametric Estimation.I. INTRODUCTIONA. System Identification Overview and MotivationsThe objective of system identification is to capture the dynamic behaviour of a system based on measured data [1]. In a rigorousmathematical sense, system identification involves the construction of the model that most closely resembles the dynamiccharacteristics of the system (here, SMPC), based on observed data [2]. Typically, a frequency rich signal is injected into thecontrol loop which, along with measurement of the resultant system output, is “processed” to derive a representative system model[3]. The system of interest is normally treated as a black-box model. The model structures are classified into two types: black box
2and grey box [2]. In the black box model, there is no prior information about the internal constituents of the system or the physicalmodelling of the system. Here, the choice of the model structure and the estimation of the parameters of the system areaccomplished based on observed data from the system [4, 5]. When the error between the real system output and the correspondingmodel output is minimised an accurate model of deemed to have been obtained. In the grey box model, the system dynamics andthe model structure are partially known in advance. The remaining unknown coefficients are estimated from the measured data.This prior information can be used as a benchmark to analyse the estimated model. In addition, it can improve the convergence ofthe applied algorithm. As an illustrative example, power converter parameters such as the output capacitance, or inductance, canbe used as known coefficients and initially utilised to calibrate the grey box model [6].In general, there are also two categories of system identification technique; on-line and off-line system identification [3, 7, 8].In the on-line paradigm, real-time data is obtained and used immediately to identify the unknown characteristics of the system.Recursive Least Squares (RLS) is perhaps the most recognisable method of on-line system identification. Adaptive control schemesincorporate this approach to adapt the controller gains at regular intervals. This is accomplished in two phases. In the first step,system performance is monitored, and the dynamic characteristics of the closed loop system are actively identified, providing realtime estimation of the model parameters. In the second step, the control parameters are fine-tuned according to the uncertaintiesof the system and this results in profound improvement in the dynamic performance of the system [9]. On-line health monitoringand fault detection are advanced features which can be incorporated into this structure. In the off-line paradigm, measured data isstored in memory; a typical approach uses a block array of memory. Once full, the array of observed signals is post-processed toestablish the system model. This process is often referred to as “batch estimation” and can be adopted when modelling highlycomplex systems [7]. The estimated model is then used to design the desired control loop to achieve specific dynamics [3].A large body of research has been carried out in the field of system identification for DC-DC Switch Mode Power Converter(SMPC) applications. Key motivations for applying system identification techniques, include:1) Mathematical modelling: Many approaches establish an average model based on linear analysis. It is significantly morecomplicated to establish an accurate SMPCs model considering the intrinsic non-linearity of the system [10, 11].2) Fundamental Control System Design: Many control approaches rely on an accurate model of the system (often representedas a transfer function) to design a robust controller; for instance, the well-established pole placement technique [12, 13].3) Advanced self-tuning and real time adaptive control design. A major challenge in complex systems is overcoming systemvariability. In SMPCs uncertainties arise from ageing effects, component tolerances, parasitic elements, and unpredictable timevarying load changes [14-16].
34) Real time monitoring of systems and devices. Real time monitoring facilitates, new condition monitoring, and fault detectionschemes; for example, temperature monitoring of power devices, short/open circuit detection, and capacitor failure [17-20].All these functions can now readily be implemented and applied in power electronics applications due to the proliferation ofnew low-cost, high performance Digital Signal Processors (DSPs) and Field Programmable Gate Arrays (FPGAs)[21].Enhancements in digital hardware and modern software tools enable power electronics control engineers to develop a wide varietyof system identification and control algorithms [22]. As a result, system identification for advanced SMPC design and control isgaining both academic and industrial interest [23].B. Fundamental Challenges in System Identification of SMPCsThere are several fundamental challenges in system identification of SMPCs [24], these are linked to:1)The computation complexity of the estimation algorithms.2)Suitability for on-line and real time implementation with closed loop operation.3) Speed and accuracy of the estimation process.4)Cost of implementation.5)Ability to deal with rapid real time changes.6) Minimising the effect on the output of SMPC.Fig.1 summarises recent innovations on system identification for SMPCs to address these implementation challenges. In thispaper, we classify the literature according to the system identification methodology (parametric or non-parametric) adopted, andthe fundamental technique applied. As shown in Fig.1, parametric estimation is divided into three schemes; iterative/recursiveschemes, non-iterative schemes, parametric modelling schemes. Likewise, non-parametric schemes are divided into three:correlation estimation schemes, network-analyser schemes, and power spectrum density (PSD) schemes. Finally, dual estimationmethods are also shown Fig.1, which use both system identification structures (parametric/ non-parametric).
4System Parametric BasedModelling Scheme[6,21,32,33,36,37,39,48,49,50]Iterative/ ametricEstimationDual StructureEstimationCorrelation AnalysisScheme[13,14,28,29,59,58,60,61]Network AnalyserScheme[12,25]Power SpectrumDensity Scheme[16][24,30,63,60]Fig.1. Advances in system identification for SMPCs.C. Contributions and Paper StructureGiven recent developments, this paper presents a comprehensive review of parametric, non-parametric, and dual hybrid systemidentification techniques for SMPC applications. This is an area where significant research is currently being carried out to developimproved identification algorithms and advanced control techniques for next generation power electronic products. Thus, such areview is timely. Finally, the existing research challenges in the field are defined and areas for further research investigation areidentified. The paper is structured as follow: Generic architecture for parametric and non-parametric system identification ofSMPCs is presented in Section II. Modelling scheme-based system identification are presented in Section III. Iterative / noniterative methodologies are explained in Sections IV and V. Non-parametric methodologies for SMPCs are demonstrated in SectionVI. Section VII presents a dual estimation scheme of SMPCs. Furthermore, application of system identification in SMPCs systemsuch as abrupt load estimation scheme and fault detection scheme are discussed in Section VIII. Finally, conclusions and discussionare summarised in Section IX.II. GENERIC SYSTEM IDENTIFICATION ARCHITECTURE & METHODOLOGY FOR SMPCSFig. 2 shows a typical SMPC closed loop controller, incorporating a generic system identification mechanism. Here, a frequencyrich signal is injected into the control loop to excite the system and the response of the system to this excitation is observed. Fromthis, an estimation of the system characteristics can be accomplished. Both system identification approaches described in this paper(ie. parametric & non-parametric) utilize the structure depicted in Fig. 2. Typically, a Pseudo- Random- Binary- Sequence (PRBS)is applied to excite the dynamics of the SMPC as it is simple to implement, frequency rich, and has similar spectral properties to
5white noise [13]. Alternatively, other external perturbations can be applied such as multitone sinusoid signal [25], blue noise signal[26], pink noise signal [6], and chirp signal [12].Sensorg (t)VinSMPCsvout(t)H(s)vos(t)c (t)PRBSA/DΔPRBS (n) vout(n) d (n)d (n) Vref (n)DPWM IController e (n) SystemIdentificationGdv(z)Fig. 2. Closed loop system identification for SMPCs.A. Non-Parametric Structure of SMPCsIn non-parametric estimation, no prior knowledge of the model structure is required to estimate the system dynamics. This isperhaps the most significant advantage of non-parametric estimation schemes [3]. In addition, the level of complexity of nonparametric methods is often quite low, making them relatively easy to implement [2, 5, 8]. However, non-parametric methods aresensitive to noise and an appropriate excitation signal is normally required to achieve accurate estimation. Therefore, acquisitionof long data sequences is essential to overcome these issues and as a result the identification process can take significant time tocomplete [3, 27]. Practically, this restricts a non-parametric schemes ability to identify rapid system variations, such as an abruptload change in an SMPC system. Also, it hinders the continuous iterative estimation of the system model, which is imperative forreal-time adaptive control design. Furthermore, inaccuracies in the estimated parameters may be more significant in the discretedomain, as a consequence of the transformation from the s-to-z domain and the effects of quantization [3, 27]. Normally, theidentification process is activated during the steady-state period, facilitating the determination of the average linear model of theSMPC [28]. In any system identification scheme, the identification procedure starts with injecting an excitation signal, and thensampling the experimental input and output data of the unknown system. In DC-DC SMPCs, the output-to-voltage control modelis commonly identified, thus the data to be processed is the output, vout(n), and the excited signal, dI(n), (see Fig. 2). The measureddata is passed to the pre-processing stage, where signal conditioning and filtering takes place to remove unwanted noisecomponents (Fig. 3) [3]. The dynamic characteristics of the SMPC can be estimated using conventional time-domain or frequencydomain analysis [2]. However, in SMPC literature, the frequency response of the system can be estimated by initially determining
6the impulse response using cross correlation techniques and then applying FFT analysis (as shown in Fig. 3). This facilitates asimpler, lower cost solution, which is essential in these applications [29]. However, in this approach, direct correlation betweenthe input and output signals cannot be assumed [3].SMPC NormalOperationID EnableSteady- State Period,PRBS InjectionCollect and Store theExcited Input/ OutputDataDataPre- ProcessingData0Time Domain AnalysisP(t)tdBFrequency DomainAnalysisP(f)0fFig. 3. Non-parametric identification procedure of SMPC.e(n)H(z)v(n)u(n)P(z)y(n) Fig. 4. General linear model transfer function.As shown in Fig. 4, the linear time invariant discrete system can be expressed as [29]: 𝑦(𝑛) 𝑝(𝑘)𝑢(𝑛 𝑘) 𝑣(𝑛)(1)𝑘 1Here, 𝑢(𝑛) is the sampled input signal, 𝑦(𝑛) is the discrete output signal, 𝑝(𝑘) is the discrete impulse response of the system, 𝑒(𝑛)is noise and 𝑣(𝑛) is the disturbance signal (in Fig. 4, ℎ(𝑛) is the discrete impulse response of the noise). From (1), the crosscorrelation between the input 𝑢(𝑛) and the output y(n) can be described as:
7 𝐑 𝑢𝑦 (𝑚) 𝑢(𝑛)𝑦(𝑛 𝑚) 𝑝(𝑛)𝐑 𝑢𝑢 (𝑚 𝑛) 𝐑 𝑢𝑣 (𝑚)𝑛 1(2)𝑛 1Where, 𝐑 𝑢𝑢 (𝑚) is the auto-correlation of u(n) and 𝐑 𝑢𝑣 (𝑚) is the cross-correlation between the input and the disturbance. Twoconditions should be considered for valid non-parametric estimation of the impulse response [29]:1) The input 𝑢(𝑛) and disturbance 𝑣(𝑛) are uncorrelated, therefore 𝐑 𝑢𝑣 (𝑚) 0.2) 𝐑 𝑢𝑢 (𝑛) is the auto-correlation of a white noise input signal and thus 𝐑 𝑢𝑢 (𝑚) 𝛿(𝑛). Consequently, equation (2) can bewritten as [5]:𝐑 𝑢𝑦 (𝑚) 𝑝(𝑚)(3)If the conditions in (1 & 2) are met, then the frequency response of the SMPC can be identified by performing frequency analysison the output to (3), for example by taking the FFT [29]:𝐹𝐹𝑇{𝐑 𝑢𝑦 (𝑚)} 𝑃(𝑓)(4)B. Parametric Estimation of SMPCsIn parametric estimation schemes, the main objective is to determine the optimal parameters that best describe the unknownmodel of the system. One of the main drawbacks of this scheme is that a model structure must be defined in advance [14].Fortunately for many SMPCs topologies, such as DC-DC buck, boost, or buck-boost converter, the candidate model is wellrecognised and normally represented as a simple second order model [30]. Higher order models can be applied, which may lead toenhanced model accuracy, however they increase computation burden. Likewise, to alleviate issues such as electromagneticinterference in SMPCs, additional harmonic filtering elements are added to the circuit [31]. This can potentially change thecandidate model (e.g. higher order model, or input to output voltage model is required) and thus increase the complexity of theidentification process. Identical to non-parametric approaches, proper excitation is imperative to ensure accurate convergence ofthe estimated parameters. Many different algorithms can be used to estimate the system parameters; Least Mean Square (LMS),Recursive Least Square (RLS), and subspace based methods are perhaps some of the dominant algorithms [2, 5, 32]. Thesealgorithms provide a simple adaptive scheme which is capable of rapid convergence rate, good estimation accuracy, and robusttracking ability in the event of system parameter changes [33]. However, the final solution is normally dependent upon a matrixinversion operation, which is computationally heavy and presents implementation difficulties. For RLS algorithms, matrixinversion can usually be avoided using matrix inversion lemma, there is still considerable operational complexity at each samplinginstant [34]. To reduce the computation burden, an approximation method to the matrix inversion operation such DCD-RLS
8algorithm can be considered [3]. With parametric estimation techniques, advanced control techniques such as pole placement andmodel reference control can easily be integrated with the estimation method [14]. Furthermore, direct digital control designmethods can be applied [3]. This can substantially reduce errors attributable to s-domain to z-domain transformationapproximations [35]. Furthermore, the model can be estimated on-line and in closed loop form, and typically has low sensitivityto noise and disturbance. This is a distinct advantage over many non-parametric identification techniques [3].As previously described, the candidate model of the unknown system is derived in advance. Fig. 5 represents the modellingprocedure of the unknown system. After a pre-processing step the model structure is selected, and the order of the model is defined.This may be accomplished from prior knowledge of the system. Thus, the selected model may be considered as a “grey box” model[6]. The optimisation algorithm is then applied to estimate the parameters of the model. The estimated model provides a best fitwith the pre-processed data. This can be achieved by comparing the estimated output data with the measured data. The differenceis known as a modelling error. If the modelling error is within a defined specification, the model is deemed acceptable and theparameters may be estimated. Otherwise, the process is repeated by selecting a new model or carefully considering the input andoutput data to determine whether any pre-processing or filtering is required [3]. Fortunately, the analytical discrete model for manycommon SMPC topologies is understood and well defined in existing literature. For simplicity, the Auto Regressive MovingAverage (ARMA) filter is a popular model employed to estimate the parameters of conventional SMPC topologies. The genericARMA model is represented in (5) [3].𝐺(𝑧) 𝑘 𝑁𝑌(𝑧)𝑏1 𝑧 1 𝑏2 𝑧 2 𝑏𝑁 𝑧 𝑁𝑘 1 𝑏𝑘 𝑧 𝑘1 𝑎1 𝑧 1 𝑎2 𝑧 2 𝑎𝑀 𝑧 𝑀𝑈(𝑧) 1 𝑀𝑘 1 𝑎𝑘 𝑧(5)Equation (5) can also be written in difference form as:𝑁𝑀𝑦(𝑛) 𝑏𝑘 𝑢(𝑛 𝑘) 𝑎𝑘 𝑦(𝑛 𝑘)𝑘 0(6)𝑘 1From which, the data and parameters vectors may be expressed as:𝛗 [ 𝑦(𝑛 1) 𝑦(𝑛 𝑁), 𝑢(𝑛 1)𝛉 [𝑎1 𝑎𝑁 , 𝑏1 𝑏𝑀 ]𝑇𝑢(𝑛 𝑀)]𝑇(7)And the estimated output is calculated in regression form by:𝑦̂ 𝛗𝑇 𝛉(8)
9Normal operation ofSMPCInjecting a PRBSInput and output datacollectionDataPre-processingProcessed DataModel structureselectionApply the identificationalgorithmModel validationNoBest fitModelYesFig. 5. Parametric identification procedure of SMPC.Referring back to Fig. 2, and once the model of the unknown system is selected, parametric identification algorithms beginprocessing the input and output signals on a sample-by-sample basis. Unlike non-parametric schemes, any system changes canusually be detected quickly based on the real time measurement data. In SMPC digital control loop design, the captured data istypically the output voltage, 𝑣𝑜𝑢𝑡 (𝑛), and the excited control action signal, 𝑑𝐼 (𝑛) (leading to the duty cycle-to-output voltagetransfer function); however, inductor current or capacitor voltage can also be used [6]. As shown in Fig. 6, at each iteration cycleprediction error methods such as RLS algorithms seek to minimise the error between the real system 𝑦(𝑛) and the estimated modelŷ(𝑛). This error is known as the prediction error 𝜀(𝑛) [3, 33]:𝜀(𝑛) 𝑦(𝑛) 𝑦̂(𝑛)(9)
10UnknownSystemy(n)u(n) ModelStructureEstimated parametersa1, a2, b1, b2 ., aN ,bMε(n) ep(n)ŷ(n)AdaptationAlgorithmFig. 6. General block diagram of parametric identification.As discussed, much research has been carried out in the field of parametric system identification of SMPCs [20, 36-39].Unfortunately, many of the presented methods require significant signal processing to implement and this eventually has a costpenalty for the target application. Furthermore, the computational complexity impacts upon microprocessor execution time, andthis in turn makes it difficult to ado
of system identification and control algorithms [22]. As a result, system identification for advanced SMPC design and control is gaining both academic and industrial interest [23]. B. Fundamental Challenges in System Identification of SMPCs . There are several fundamental challenges in system identification of SMPCs [24], these are linked to:
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